CN110673477A - Design method of discrete time power attraction controller adopting interference difference suppression strategy - Google Patents

Design method of discrete time power attraction controller adopting interference difference suppression strategy Download PDF

Info

Publication number
CN110673477A
CN110673477A CN201910920607.4A CN201910920607A CN110673477A CN 110673477 A CN110673477 A CN 110673477A CN 201910920607 A CN201910920607 A CN 201910920607A CN 110673477 A CN110673477 A CN 110673477A
Authority
CN
China
Prior art keywords
interference
error
time
controller
reference signal
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN201910920607.4A
Other languages
Chinese (zh)
Inventor
孙明轩
李旺
王晗
邹胜祥
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Zhejiang University of Technology ZJUT
Original Assignee
Zhejiang University of Technology ZJUT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Zhejiang University of Technology ZJUT filed Critical Zhejiang University of Technology ZJUT
Priority to CN201910920607.4A priority Critical patent/CN110673477A/en
Publication of CN110673477A publication Critical patent/CN110673477A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Abstract

A design method of a discrete time power attraction controller adopting an interference difference suppression strategy comprises the steps that a given module generates a reference signal; constructing a corresponding interference differential compensation feedback link according to the specific form of a given reference signal, wherein an output signal of the interference differential compensation feedback link is used for interference compensation in a digital controller; and constructing an ideal error dynamic state based on the power law of attraction, designing a digital controller according to the ideal error dynamic state, and taking a signal obtained by calculation of the current controller as the input of a servo object. The specific controller parameter setting can be carried out according to the indexes of the convergence performance of the representation system, and specific expressions of a steady-state error band, an absolute attraction layer, a monotone subtraction area and the maximum convergence step number of the system tracking error entering the steady-state error band for the first time in the process of representing the convergence of the tracking error are provided. The power attraction controller design method provided by the invention adopts corresponding interference difference compensation measures according to the given reference signal and improves the tracking precision of the servo system by inhibiting interference.

Description

Design method of discrete time power attraction controller adopting interference difference suppression strategy
Technical Field
The invention relates to a design method of a discrete time power attraction controller adopting an interference difference suppression strategy, which is suitable for a position servo system and other industrial occasions containing periodic operation processes.
Background
The attraction law method is different from an approach law method of discrete sliding mode control. The main differences between the two are as follows: replacing a switching function by the tracking error and replacing a switching surface by the original point by the attraction law method; the approach law method requires a finite time to reach the switching surface, while the attraction law method requires a finite time to reach the origin; the closed-loop system designed by the attraction law method still has robust performance related to parameter drift and external interference, only the sliding mode control focuses on invariance of sliding mode motion, and the attraction law method pursues invariance of system steady state.
The attraction law method directly adopts a tracking error signal, and the controller is more direct and simpler in design. The attraction law reflects the expected dynamic characteristics of the system error when disturbance is not considered; in the presence of interference, a controller designed directly according to the attraction law cannot be implemented. The interference suppression measures can be 'embedded' into the attraction law, and ideal error dynamics with the disturbance suppression effect are constructed. The digital controller is designed according to the constructed ideal error dynamic equation, and the dynamic process of the closed-loop system is determined by the ideal error dynamic equation and has the expected tracking performance represented by the ideal error dynamic equation.
When the discrete controller is designed by an attraction law method, indexes describing transient and steady-state behaviors of the tracking error can be dynamically given by an ideal error, and the indexes specifically comprise the following four indexes: a steady state error band, an absolute attraction layer, a monotonically decreasing region, and a maximum number of steps required to first converge to the steady state error band. The specific values of the four indexes depend on the controller parameter and the equivalent interference signal, the controller parameter and the equivalent interference signal have different boundaries, and the values of the four indexes are also different. Once the ideal error dynamic form is given, specific expressions of four indexes can be given in advance for parameter setting of the controller.
Disclosure of Invention
The invention provides a design method of a discrete time power attraction controller adopting an interference difference suppression strategy. In order to enable the closed-loop system to have the preset expected error tracking performance, an interference difference suppression strategy is adopted and embedded into the power attraction law to construct an ideal error dynamic with disturbance suppression capability, so that a controller is designed, the closed-loop system has the characteristics depicted by the ideal error dynamic to improve the control performance, and the motor servo system realizes high-speed and high-precision tracking. The invention specifically provides specific expressions of four indexes, namely a steady-state error band, an absolute attraction layer, a monotone decreasing area and a maximum step number required by first convergence to the steady-state error band, and the expressions can be used for guiding the parameter setting of the controller.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a design method of a discrete time power attraction controller adopting an interference difference suppression strategy comprises the following steps:
step 1, giving reference signal rkFor a polynomial of the time variable k, M representing the highest power of the polynomial, three reference signals are as follows:
1) square wave signal, M ═ 0
Figure BDA0002217435960000021
2) Triangular wave signal, M1
Figure BDA0002217435960000022
3) Curve S, M being 3
Figure BDA0002217435960000023
Wherein, A is amplitude, and N is sampling times of the reference signal in one period;
step 2, constructing ideal error dynamic state, giving out power attraction law,
ek+1＝(1-ρ)ek-ε|ek|αsgn(ek) (4)
wherein e isk＝rk-ykDenotes time k, ek+1Represents the tracking error at the moment of k +1, rho, epsilon and constants respectively representing the attraction speed, alpha is an attraction index, and the corresponding value range is as follows: 0 < rho < 1, epsilon >0，0＜α＜1。
The interference suppression measure is embedded into the above-mentioned attraction law, and the following ideal error dynamics are constructed
Wherein d isk+1Is the equivalent interference at the time k +1,
Figure BDA0002217435960000025
for compensating for the equivalent interference, and for compensating for the equivalent interference,the error is compensated for equivalent interference.
Step 3. interference difference compensation strategy
Take the equivalent interference compensation effect asDefining an equivalent interference for a particular reference signal in the form of
Equivalent interference signal when M is 0
dk+1＝wk+1(6)
Equivalent interference signal when M is 1
dk+1＝wk+1-wk(7)
Equivalent interference signal when M is 3
dk+1＝[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)](8)
Wherein, wk+1Interference at time k + 1.
Defining the step number of the interference difference as L, wherein L represents that the interference compensation error comprises L interferences at successive moments, and the two-step interference difference d is shown in formula (6)k+1-dk＝wk+1-wkComprising wk+1And wkTwo-time interference, in order to effectively suppress interference, when selecting equivalent interference, the following condition should be satisfied
Wherein the content of the first and second substances,
Figure BDA0002217435960000033
is the smallest integer not less than;
step 4. controller design
According to the ideal error dynamics (5) and the equivalent interference signal dk+1The following controller expression is given:
1) for square wave reference signal type
Figure BDA0002217435960000034
Wherein, F (q)-1)＝(q-d+1B(q-1)-b1)。
2) For triangular wave reference signal type
Figure BDA0002217435960000035
Wherein the content of the first and second substances,
Figure BDA0002217435960000036
3) for S-curve reference signal formula
Figure BDA0002217435960000041
Wherein
Figure BDA0002217435960000042
In formulae (10) to (12), A (q)-1)、B(q-1) For serving systems
A(q-1)yk＝q-dB(q-1)uk+wk(13)
With respect to q-1Has more parametersThe term:
A(q-1)＝1+a1q-1+a2q-2+……+anq-n
B(q-1)＝b1q-1+b2q-2+……+bmq-m
wherein u iskAnd ykInput and output signals at time k of the servo system, d represents a delay factor, q-1For one-step delay operator, m and n are respectively A (q)-1)、B(q-1) Order of (b)1≠0，1≤m≤n。
Further, the method further comprises:
step 5. Performance analysis
And giving specific expressions of four indexes, namely a steady-state error band, an absolute attraction layer, a monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time, and being used for describing the tracking performance of the system and guiding the parameter setting of the controller, wherein the steady-state error band, the absolute attraction layer, the monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time are defined as follows:
monotonous decreasing region deltaMDR: when e iskGreater than 0 at this boundary, ekThe same number is decreased, namely the following conditions are met:
Figure BDA0002217435960000043
absolute attraction layer ΔAAL: absolute value of system tracking errorkIf | is greater than this boundary, its | ekI, monotonically decreases, i.e. the condition is satisfied:
Figure BDA0002217435960000044
steady state error band ΔSSE: when the system error once converges into the boundary, the error is stabilized in the region, that is, the following condition is satisfied:
Figure BDA0002217435960000059
maximum number of convergence steps
Figure BDA0002217435960000051
The tracking error passes through at most
Figure BDA0002217435960000052
Step into the steady state error band.
Equivalent interference compensation error satisfaction
Figure BDA0002217435960000053
The expression of each index is as follows:
(1) monotonous decreasing region deltaMDR
ΔMDR＝max{ΔMDR1,ΔMDR2} (17)
Figure BDA0002217435960000054
Wherein, DeltaMDR1And ΔMDR2Are all real and are determined by equation (18).
(2) Absolute attraction layer ΔAAL
ΔAAL＝max{ΔAAL1,ΔAAL2} (19)
Figure BDA0002217435960000055
Wherein, DeltaAAL1And ΔAAL2Are all real and are determined by equation (20).
(3) Steady state error band ΔSSE
ΔSSE＝max{ΔSSE1,ΔSSE2} (21)
Figure BDA0002217435960000056
Wherein, DeltaSSE1And ΔSSE2Are all real, and are of the formula(22) And (4) determining.
For aiming at
Figure BDA0002217435960000057
The expression of each index is as follows:
monotonous decreasing region deltaMDR
ΔMDR＝max{ΔMDR1,ΔMDR2} (23)
1) When in use
Figure BDA0002217435960000058
Time of flight
Figure BDA0002217435960000061
2) When in useTime of flight
Figure BDA0002217435960000064
3) When in use
Figure BDA0002217435960000066
Time of flight
Wherein
Absolute attraction layer ΔAAL
ΔAAL＝max{ΔAAL1,ΔAAL2} (30)
1) When in use
Figure BDA0002217435960000071
Time of flight
Figure BDA0002217435960000072
Figure BDA0002217435960000073
2) When in useTime of flight
Figure BDA0002217435960000076
3) When in useTime of flight
Wherein
Figure BDA0002217435960000081
Steady state error band ΔSSE
1) When in use
Figure BDA0002217435960000082
Or ΔAAL≥δSSETime of flight
ΔSSE＝ΔAAL(37)
2)
Figure BDA0002217435960000083
Time of flight
Figure BDA0002217435960000084
Wherein deltaSSEIs an equationRoot of Zhengguo;
number of convergence steps
Figure BDA00022174359600000810
Figure BDA0002217435960000087
Wherein e is0In order to be the initial value of the tracking error,represents the smallest integer no less than.
The technical conception of the invention is as follows: a design method of a discrete time power attraction controller adopting an interference difference suppression strategy is provided. And defining equivalent interference according to a given reference signal, and embedding an interference suppression measure into a power attraction law to form ideal error dynamics with interference suppression effect. The digital controller is dynamically designed according to the ideal error to realize accurate tracking of a given reference signal.
The invention has the following beneficial effects: according to the given reference signal, a corresponding interference difference compensation measure is adopted, and the tracking accuracy is improved by suppressing interference.
Drawings
FIG. 1 is a block diagram of a servo system.
In FIGS. 2 to 4, rk＝10sin(2πfkTs)deg，f＝1Hz，TsThe numerical simulation result of the controller equation (33) is used when Δ is 0.005s and Δ is 0.3, and fig. 2 shows the tracking error signal e when ρ is 0.3 and ∈ is 0.1k(ii) a Fig. 3 shows a tracking error signal e when ρ is 0.5 and ∈ is 0.15k(ii) a FIG. 4 is interference error compensation
FIGS. 5-7 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1 as equation (1), the numerical simulation result of controller equation (33) is used, where fig. 5 shows the reference signal rkAnd the output signal yk(ii) a FIG. 6 shows a tracking error signal ek(ii) a FIG. 7 is interference error compensation
Figure BDA0002217435960000091
FIGS. 8-10 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1, the numerical simulation of the controller formula (33) is employed as formula (2), where fig. 8 is the reference signal rkAnd the output signal yk(ii) a FIG. 9 shows a tracking error signal ek(ii) a FIG. 10 is interference error compensation
Figure BDA0002217435960000092
FIGS. 11-13 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1 as equation (2), the numerical simulation result of controller equation (34) is used, where fig. 11 shows the reference signal rkAnd the output signal yk(ii) a FIG. 12 shows a tracking error signal ek(ii) a FIG. 13 is interference error compensation
Figure BDA0002217435960000093
FIGS. 14-16 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1 as equation (3), the numerical simulation result of controller equation (33) is used, where fig. 14 shows the reference signal rkAnd the output signal yk(ii) a FIG. 15 shows a tracking error signal ek(ii) a FIG. 16 is interference error compensation
Figure BDA0002217435960000094
FIGS. 17-19 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1 as equation (3), the numerical simulation result of controller equation (34) is used, where fig. 17 shows the reference signal rkAnd the output signal yk(ii) a FIG. 18 shows a tracking error signal ek(ii) a FIG. 19 is interference error compensation
FIGS. 20-22 show a reference signal rkWhen a is 20, ρ is 0.3, and ∈ is 0.1 as equation (3), the numerical simulation result of controller equation (35) is used, where fig. 20 shows the reference signal rkAnd the output signal yk(ii) a FIG. 21 shows a tracking error signal ek(ii) a FIG. 22 is interference error compensation
Figure BDA0002217435960000096
FIGS. 23-25 show a reference signal rkAs in formula (1), A ═ 15deg, TsWhen ρ is 0.6 and ∈ is 0.3 for 5ms, the result of the experiment using controller equation (33) is employed, where fig. 23 shows the reference signal rkAnd the output signal ykFIG. 24 shows a tracking error signal ekFIG. 25 shows a tracking error signal ekA histogram of (a).
FIGS. 26-28 show a reference signal rkAs in formula (2), A ═ 110deg, TsWhen ρ is 0.6 and ∈ is 0.3 for 5ms, the experimental result of the controller equation (33) is used, where fig. 26 shows the reference signal rkAnd the output signal ykFIG. 27 shows a tracking error signal ekFIG. 28 shows a tracking error signal ekA histogram of (a).
FIGS. 29-31 show the reference signal rkAs in formula (2), A ═ 110deg, TsThe experimental results of the controller equation (34) are employed when ρ is 0.6 and ∈ is 0.3 for 5ms, and fig. 29 is a referenceSignal rkAnd the output signal ykFIG. 30 shows a tracking error signal ekFIG. 31 shows a tracking error signal ekA histogram of (a).
FIGS. 32-34 show a reference signal rkAs in formula (3), A ═ 60deg, TsWhen ρ is 0.6 and ∈ is 0.3 for 5ms, the experimental result of the controller equation (33) is used, where fig. 32 shows the reference signal rkAnd the output signal ykFIG. 33 shows a tracking error signal ekFIG. 34 shows a tracking error signal ekA histogram of (a).
FIGS. 35-37 show a reference signal rkAs in formula (3), A ═ 60deg, TsWhen ρ is 0.6 and ∈ is 0.3 for 5ms, the experimental result of the controller equation (34) is used, and fig. 35 shows the reference signal rkAnd the output signal ykFIG. 36 shows a tracking error signal ekFIG. 37 shows a tracking error signal ekA histogram of (a).
FIGS. 38-40 show a reference signal rkAs in formula (3), A ═ 60deg, TsWhen ρ is 0.6 and ∈ is 0.3 for 5ms, the experimental result of controller equation (35) is used, where fig. 38 shows the reference signal rkAnd the output signal ykFIG. 39 shows a tracking error signal ekFIG. 40 shows a tracking error signal ekA histogram of (a).
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings.
Referring to fig. 1, a method for designing a discrete time controller power law of attraction by using an interference difference suppression strategy includes the following steps:
reference signal rkIs a polynomial of a time variable k, M representing the highest power of the polynomial; the three reference signals are as follows:
1) square wave signal, M ═ 0
Figure BDA0002217435960000101
2) Triangular wave signal, M1
Figure BDA0002217435960000102
3) Curve S, M being 3
Figure BDA0002217435960000103
Wherein, A is amplitude, and N is sampling times of the reference signal in one period;
step 2, constructing ideal error dynamic state
For the law of attraction of power
ek+1＝(1-ρ)ek-ε|ek|αsgn(ek) (4)
Wherein e isk＝rk-ykDenotes time k, ek+1Represents the tracking error at the moment of k +1, rho, epsilon and constants respectively representing the attraction speed, alpha is an attraction index, and the corresponding value range is as follows: rho is more than 0 and less than 1, and epsilon is more than 0;
the interference suppression measure is embedded into the above-mentioned attraction law, and the following ideal error dynamics are constructed
Wherein d isk+1Is the equivalent interference at the time k +1,
Figure BDA0002217435960000112
for compensating for the equivalent interference, and for compensating for the equivalent interference,
Figure BDA0002217435960000113
compensating the error for the equivalent interference;
step 3. interference difference compensation strategy
Take the equivalent interference compensation effect as
Figure BDA0002217435960000114
Defining an equivalent interference for a particular reference signal in the form of
Equivalent interference signal when M is 0
dk+1＝wk+1(6)
Equivalent interference signal when M is 1
dk+1＝wk+1-wk(7)
Equivalent interference signal when M is 3
dk+1＝[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)](8)
Wherein, wk+1Interference at time k + 1;
defining the step number of the interference difference as L, wherein L represents that the interference compensation error comprises L interferences at successive moments, and the two-step interference difference d is shown in formula (6)k+1-dk＝wk+1-wkComprising wk+1And wkTwo-time interference, in order to effectively suppress interference, when selecting equivalent interference, the following condition should be satisfied
Figure BDA0002217435960000115
Wherein the content of the first and second substances,
Figure BDA0002217435960000116
is the smallest integer not less than;
step 4. controller design
According to the ideal error dynamics (5) and the equivalent interference signal dk+1The following controller expression is given:
1) for square wave reference signal type
Figure BDA0002217435960000121
Wherein, F (q)-1)＝(q-d+1B(q-1)-b1)。
2) For triangular wave reference signal type
Figure BDA0002217435960000122
Wherein the content of the first and second substances,
Figure BDA0002217435960000123
3) for S-curve reference signal formula
Figure BDA0002217435960000124
Wherein
Figure BDA0002217435960000125
In formulae (10) to (12), A (q)-1)、B(q-1) For serving systems
A(q-1)yk＝q-dB(q-1)uk+wk(13)
With respect to q-1The parameter polynomial of (2):
A(q-1)＝1+a1q-1+a2q-2+……+anq-n
B(q-1)＝b1q-1+b2q-2+……+bmq-m
wherein u iskAnd ykInput and output signals at time k of the servo system, d represents a delay factor, q-1For one-step delay operator, m and n are respectively A (q)-1)、B(q-1) Order of (b)1≠0，1≤m≤n。
Further, the method further comprises:
step 5. Performance analysis
And giving specific expressions of four indexes, namely a steady-state error band, an absolute attraction layer, a monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time, and being used for describing the tracking performance of the system and guiding the parameter setting of the controller, wherein the steady-state error band, the absolute attraction layer, the monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time are defined as follows:
monotonous decreasing region deltaMDR: when e iskGreater than 0 at this boundary, ekThe same number is decreased, namely the following conditions are met:
Figure BDA0002217435960000131
absolute attraction layer ΔAAL: absolute value of system tracking errorkIf | is greater than this boundary, its | ekI, monotonically decreases, i.e. the condition is satisfied:
Figure BDA0002217435960000132
steady state error band ΔSSE: when the system error once converges into the boundary, the error is stabilized in the region, that is, the following condition is satisfied:
Figure BDA0002217435960000133
maximum number of convergence steps
Figure BDA0002217435960000134
The tracking error passes through at most
Figure BDA0002217435960000135
Step into the steady state error band.
For aiming at
Figure BDA0002217435960000136
The expression of each index is as follows:
monotonous decreasing region deltaMDR
ΔMDR＝max{ΔMDR1,ΔMDR2} (17)
1) When in use
Figure BDA0002217435960000137
Time of flight
Figure BDA0002217435960000139
2) When in use
Figure BDA00022174359600001310
Time of flight
Figure BDA00022174359600001311
Figure BDA0002217435960000141
3) When in use
Figure BDA0002217435960000142
Time of flight
Figure BDA0002217435960000143
Wherein
Figure BDA0002217435960000144
Figure BDA0002217435960000145
Absolute attraction layer ΔAAL
ΔAAL＝max{ΔAAL1,ΔAAL2} (24)
1) When in use
Figure BDA0002217435960000146
Time of flight
Figure BDA0002217435960000147
Figure BDA0002217435960000148
2) When in use
Figure BDA0002217435960000151
Time of flight
Figure BDA0002217435960000152
Figure BDA0002217435960000153
3) When in use
Figure BDA0002217435960000154
Time of flight
Figure BDA0002217435960000155
Wherein
Figure BDA0002217435960000156
Figure BDA0002217435960000157
Steady state error band ΔSSE
1) When in use
Figure BDA0002217435960000158
Or ΔAAL≥δSSETime of flight
ΔSSE＝ΔAAL(30)
2)
Figure BDA0002217435960000159
Time of flight
Figure BDA00022174359600001510
Wherein deltaSSEIs an equation
Figure BDA00022174359600001511
The root of Zhengguo.
Number of convergence steps
Figure BDA00022174359600001512
Wherein e is0In order to be the initial value of the tracking error,
Figure BDA0002217435960000162
represents the smallest integer no less than.
And calculating boundary values according to the expressions (16) to (31) to determine the tracking performance of the closed-loop system.
The permanent magnet synchronous motor device executes a position accurate tracking task, and a digital controller is designed for position loop control, wherein a current loop and a speed loop controller are provided by an ELMO driver; the position loop controller is provided by a DSP development board TMS320F 2812.
Through a least square identification method, the following mathematical model of the permanent magnet synchronous servo system is given
yk+1-1.8949yk+0.8949yk-1＝1.7908uk-0.5704uk-1+wk+1
When M is 0, it can be obtained from formula (10)
Figure BDA0002217435960000163
When M is 1, it can be obtained from formula (11)
Figure BDA0002217435960000164
For M ═ 3, can be obtained from formula (12)
Figure BDA0002217435960000165
The effectiveness of interference difference compensation measures in a discrete servo system is verified through numerical simulation and experimental results.
The simulation is divided into two parts, the first part verifies three boundary values, and the second part verifies the interference suppression effect of the interference difference compensation measure.
(1) Given reference letter rk＝10sin(2πfkTs) deg, frequency f 1Hz, sampling period Ts5ms, interference wk0.15| mod (k,20) -10| +0.15| mod (k +5,20) -10 |. Under the action of the controller formula (33), the parameters ρ and ε have different values, and the performance index of the system will also be different, as shown in FIGS. 2-3.
(i) When the controller parameter is Δ 0.3, ρ 0.3, and ∈ 0.1 (see fig. 2), the performance index is
ΔAAL＝ΔSSE＝ΔMDR＝0.7035
(ii) When the controller parameter is Δ 0.3, ρ 0.5, and ∈ 0.15 (see fig. 3), the performance index is
ΔMDR＝0.8889，ΔAAL＝ΔSSE＝0.3823
Through simulation, the result shows that the steady-state error band deltaSSEAbsolute attraction layer DeltaAALAnd a monotone decreasing region DeltaMDRThe accuracy of (2).
(2) The reference signals are respectively a square wave signal formula (1), a triangular wave signal formula (2) and an S curve formula (3), and the amplitudes A are respectively 20, 20 and 20. In order to verify that the interference difference step number L is in a full formula (9), the designed controller can realize accurate tracking of the corresponding reference signal, and the disturbance signal is selected as wk＝0.1rkSampling period TsThe controller parameter ρ is 0.3 and ∈ is 0.1 for 5 ms.
1) Reference signal rkFor equation (1), controller equation (33) is used, and the simulation results are shown in FIGS. 5-7, where ΔSSE＝0deg。
2) Reference signal rkFor equation (2), the controller is adopted as equation (33), and the simulation results are shown in FIGS. 8-10, in which ΔSSE＝0.02deg。
3) Reference signal rkFor equation (2), the controller is adopted as equation (34), and the simulation results are shown in FIGS. 11-13, in which ΔSSE＝0deg。
4) Reference signal rkFor equation (3), the controller is adopted as equation (33), and the simulation results are shown in FIGS. 14-16, in which ΔSSE＝0.03deg。
5) Reference signal rkFor equation (3), the controller is adopted as equation (34), and the simulation results are shown in FIGS. 17-19, in which ΔSSE＝0.002deg。
6) Reference signal rkFor equation (3), the controller is adopted as equation (35), and the simulation results are shown in FIGS. 20-22, in which ΔSSE＝0deg。
Through simulation (2), it is shown that a controller adopting the interference difference compensation design can realize accurate tracking of a given reference signal when M and L satisfy equation (9), and the closer L is to each other when M and L do not satisfy equation (9)
Figure BDA0002217435960000171
The better the tracking effect and the control process has no buffeting.
The control method provided by the invention is verified on a position servo device, and FIG. 1 is a block diagram of a position servo system. The reference signals are respectively a square wave signal formula (1), a triangular wave signal formula (2) and an S curve formula (3). The effects of the interference difference compensation technique were verified using controller equations (33), (34), and (35), respectively. Sampling period T in the experimentsThe controller parameter ρ is 0.6, and ∈ is 0.5 for 5ms, and the amplitudes a of the reference signals equation (1), equation (2), and equation (3) are 15deg, 110deg, and 60deg, respectively. The experimental results are as follows:
1) reference signal rkThe experimental results are shown in fig. 23-25 using the controller (33) according to equation (1). The system tracking error is 0.1 deg.
2) Reference signal rkThe results of the experiment are shown in FIGS. 26-28 using the controller (33) as in equation (2). The tracking error of the system is 0.05 deg.
3) Reference signal rkThe experimental results are shown in fig. 29-fig. 31 using the controller (34) as in formula (2). System trackingThe error was 0.05 deg.
4) Reference signal rkThe experimental results are shown in fig. 32-34 using the controller (33) as in formula (3). The system tracking error is 0.2 deg.
5) Reference signal rkThe results of the experiment are shown in fig. 35-37 using the controller (34) as in equation (3). The system tracking error is 0.15 deg.
6) Reference signal rkThe experimental results are shown in fig. 38-40 using the controller (35) as in equation (3). The system tracking error is 0.1 deg.
Experimental results show that when M and L satisfy the formula (9), the controller adopting the interference difference compensation design can realize accurate tracking of a given reference signal, and when M and L do not satisfy the formula (9), the closer L is
Figure BDA0002217435960000181
The better the system tracking performance.

Claims (2)

1. A method for designing a discrete-time power-of-attraction controller using an interference-difference suppression strategy, the method comprising the steps of:
step 1, giving reference signal rkFor a polynomial of the time variable k, M representing the highest power of the polynomial, three reference signals are as follows:
1) square wave signal, M ═ 0
2) Triangular wave signal, M1
Figure FDA0002217435950000012
3) Curve S, M being 3
Figure FDA0002217435950000013
Wherein, A is amplitude, and N is sampling times of the reference signal in one period;
step 2, constructing ideal error dynamic state
For the law of attraction of power
ek+1＝(1-ρ)ek-ε|ek|αsgn(ek) (4)
Wherein e isk＝rk-ykDenotes time k, ek+1Represents the tracking error at the moment of k +1, rho, epsilon and constants respectively representing the attraction speed, alpha is an attraction index, and the corresponding value range is as follows: rho is more than 0 and less than 1, and epsilon is more than 0;
embedding interference suppression measures into the attraction law to construct an ideal error dynamic
Figure FDA0002217435950000021
Wherein d isk+1Is the equivalent interference at the time k +1,
Figure FDA0002217435950000022
for compensating for the equivalent interference, and for compensating for the equivalent interference,
Figure FDA0002217435950000023
compensating the error for the equivalent interference;
step 3. interference difference compensation strategy
Take the equivalent interference compensation effect as
Figure FDA0002217435950000024
Defining an equivalent interference for a particular reference signal in the form of
Equivalent interference signal when M is 0
dk+1＝wk+1(6)
Equivalent interference signal when M is 1
dk+1＝wk+1-wk(7)
Equivalent interference signal when M is 3
dk+1＝[(wk+1-wk)-(wk-wk-1)]-[(wk-wk-1)-(wk-1-wk-2)](8)
Wherein, wk+1Interference at time k + 1;
defining the step number of the interference difference as L, wherein L represents that the interference compensation error comprises L interferences at successive moments, and the two-step interference difference d is shown in formula (6)k+1-dk＝wk+1-wkComprising wk+1And wkTwo-time interference, in order to effectively suppress interference, when selecting equivalent interference, the following condition should be satisfied
Figure FDA0002217435950000025
Wherein the content of the first and second substances,
Figure FDA0002217435950000026
is the smallest integer not less than;
step 4. controller design
According to the ideal error dynamics (5) and the equivalent interference signal dk+1The following controller expression is given:
1) for a square wave reference signal equation (1),
Figure FDA0002217435950000027
wherein, F (q)-1)＝(q-d+1B(q-1)-b1)；
2) For the triangular wave reference signal equation (2),
Figure FDA0002217435950000028
wherein the content of the first and second substances,
Figure FDA0002217435950000031
3) for the S-curve reference signal equation (3),
Figure FDA0002217435950000032
wherein
Figure FDA0002217435950000033
In formulae (10) to (12), A (q)-1)、B(q-1) For serving systems
A(q-1)yk＝q-dB(q-1)uk+wk(13)
With respect to q-1The parameter polynomial of (2):
A(q-1)＝1+a1q-1+a2q-2+……+anq-n
B(q-1)＝b1q-1+b2q-2+……+bmq-m
wherein u iskAnd ykInput and output signals at time k of the servo system, d represents a delay factor, q-1For one-step delay operator, m and n are respectively A (q)-1)、B(q-1) Order of (b)1≠0，1≤m≤n。
2. The method of claim 1, wherein the method further comprises:
step 5. Performance analysis
And giving specific expressions of four indexes, namely a steady-state error band, an absolute attraction layer, a monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time, and being used for describing the tracking performance of the system and guiding the parameter setting of the controller, wherein the steady-state error band, the absolute attraction layer, the monotone subtraction area and the maximum step number required by the tracking error entering the steady-state error band for the first time are defined as follows:
1) steady state error band ΔSSE
2) Absolute attraction layer ΔAAL
Figure FDA0002217435950000035
3) Monotonous decreasing region deltaMDR
Figure FDA0002217435950000036
4) Maximum number of convergence stepsThe tracking error passes through at most
Figure FDA0002217435950000042
Entering a steady state error band;
equivalent interference compensation error satisfactionWhen aiming at
Figure FDA0002217435950000044
The expression of each index is as follows:
monotonous decreasing region deltaMDR
ΔMDR＝max{ΔMDR1,ΔMDR2} (14)
1) When in useTime of flight
Figure FDA0002217435950000046
Figure FDA0002217435950000047
2) When in use
Figure FDA0002217435950000048
Time of flight
Figure FDA0002217435950000049
Figure FDA00022174359500000410
3) When in use
Figure FDA00022174359500000411
Time of flight
Figure FDA00022174359500000412
Wherein
Figure FDA0002217435950000051
Figure FDA0002217435950000052
2) Absolute attraction layer ΔAAL
ΔAAL＝max{ΔAAL1,ΔAAL2} (21)
1) When in useTime of flight
Figure FDA0002217435950000054
Figure FDA0002217435950000055
2) When in use
Figure FDA0002217435950000056
Time of flight
Figure FDA0002217435950000057
Figure FDA0002217435950000058
3) When in use
Figure FDA0002217435950000059
Time of flight
Figure FDA0002217435950000061
Wherein
Figure FDA0002217435950000062
Figure FDA0002217435950000063
3) Steady state error band ΔSSE
1) When in use
Figure FDA0002217435950000064
Or ΔAAL≥δSSETime of flight
ΔSSE＝ΔAAL(28)
2)
Figure FDA0002217435950000065
Time of flight
Figure FDA0002217435950000066
Wherein deltaSSEIs an equation
Figure FDA0002217435950000067
Root of Zhengguo;
number of convergence steps
Figure FDA0002217435950000069
Wherein e is0In order to be the initial value of the tracking error,
Figure FDA00022174359500000610
represents the smallest integer no less than.
CN201910920607.4A 2019-09-27 2019-09-27 Design method of discrete time power attraction controller adopting interference difference suppression strategy Pending CN110673477A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910920607.4A CN110673477A (en) 2019-09-27 2019-09-27 Design method of discrete time power attraction controller adopting interference difference suppression strategy

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910920607.4A CN110673477A (en) 2019-09-27 2019-09-27 Design method of discrete time power attraction controller adopting interference difference suppression strategy

Publications (1)

Publication Number Publication Date
CN110673477A true CN110673477A (en) 2020-01-10

Family

ID=69079510

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910920607.4A Pending CN110673477A (en) 2019-09-27 2019-09-27 Design method of discrete time power attraction controller adopting interference difference suppression strategy

Country Status (1)

Country Link
CN (1) CN110673477A (en)

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108828958A (en) * 2018-08-21 2018-11-16 浙江工业大学 It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference
CN110134010A (en) * 2019-04-17 2019-08-16 浙江工业大学 A kind of power attraction repetitive control using equivalent disturbance compensation servo-system

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108828958A (en) * 2018-08-21 2018-11-16 浙江工业大学 It is a kind of to inhibit the discrete time controller of strategy to attract rule design method without switching using interference difference
CN110134010A (en) * 2019-04-17 2019-08-16 浙江工业大学 A kind of power attraction repetitive control using equivalent disturbance compensation servo-system

Similar Documents

Publication Publication Date Title
CN109188908B (en) Digital controller design method based on exponential type non-switching attraction law
CN107544244B (en) Discrete repetitive control method for motor servo system based on elliptic attraction law and equivalent disturbance expansion state compensation
CN107797448B (en) Motor position discrete repetitive control method adopting disturbance expansion compensation
CN109450307B (en) Discrete repetitive control method for motor servo system based on similar normal distribution attraction law and adopting disturbance expansion state compensation
CN107544245B (en) Discrete repetitive control method for motor servo system adopting disturbance expansion compensation first-order inertia attraction law
CN110134010B (en) Power attraction repetitive control method adopting equivalent disturbance compensation servo system
Hou et al. Discrete-time terminal sliding-mode tracking control with alleviated chattering
CN107121932B (en) Motor servo system error symbol integral robust self-adaptive control method
CN107102634B (en) A kind of parameter Estimation and tracking and controlling method based on table servo system
CN111546346B (en) Flexible joint disturbance observation method, moment control method and equipment
CN108958041B (en) Discrete double-period repetitive control method based on hyperbolic secant attraction law
CN108828958B (en) Non-switching attraction law design method of discrete time controller adopting interference differential suppression strategy
CN110134014B (en) Equivalent disturbance compensation method for periodic servo system power attraction repetitive control
CN105387859A (en) Temperature drift error compensation method of MEMS (Micro-electromechanical System) sensor group
Durmaz et al. Sliding mode control for non-linear systems with adaptive sliding surfaces
CN110716430B (en) Servo system rapid suction repetitive control method adopting equivalent disturbance compensation
CN110658719A (en) Servo system non-switching attraction repetitive control method adopting equivalent disturbance compensation
CN110389528A (en) Data-driven MEMS gyroscope drive control method based on disturbance observation
CN109100938B (en) Discrete time controller attraction law design method adopting interference differential compensation
Trivedi et al. Roll stabilization: a higher-order sliding-mode approach
Cao et al. Robust flight control design using sensor-based backstepping control for unmanned aerial vehicles
CN111752158B (en) Second-order sliding mode control method for finite time convergence
CN110673477A (en) Design method of discrete time power attraction controller adopting interference difference suppression strategy
CN104991445B (en) A kind of motor servo system of Existence of Global Stable adaptively exports feedback robust control method
Dorwarth et al. Nonlinear model order reduction for high Q MEMS gyroscopes

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20200110